Show in each case that the series converges or diverges

I can't make out the summand in (d), and I addressed (c) in your other question.

(a)

We have for positive integers that . We also are aware that the series



converges, since it is a -series with . Since the -series converges in absolute value, the alternating series must also converge by comparison.

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(b)

By the alternating series test, this series will converge if the absolute value of the summand is increasing for some large enough and approaches zero.

We have



for all , and we also have that



(where we substituted , so that ).

Therefore (b) also converges.

Where the white dots are is where your points should be plotted.a translation is simply just moving something from one place to another. in this case, you would move each plot point of the original shape 2 units up, and 5 units to the left.